Pub Date : 2019-06-26DOI: 10.5772/intechopen.83375
O. Ozturk
Oscillation and nonoscillation theories have recently gotten too much attention and play a very important role in the theory of time-scale systems to have enough information about the long-time behavior of nonlinear systems. Some applications of such systems in discrete and continuous cases arise in control and stability theories for the unmanned aerial and ground vehicles (UAVs and UGVs). We deal with a two-dimensional nonlinear system to investigate the oscillatory behaviors of solutions. This helps us understand the limiting behavior of such solutions and contributes several theoretical results to the literature.
{"title":"Oscillation Criteria of Two-Dimensional Time-Scale Systems","authors":"O. Ozturk","doi":"10.5772/intechopen.83375","DOIUrl":"https://doi.org/10.5772/intechopen.83375","url":null,"abstract":"Oscillation and nonoscillation theories have recently gotten too much attention and play a very important role in the theory of time-scale systems to have enough information about the long-time behavior of nonlinear systems. Some applications of such systems in discrete and continuous cases arise in control and stability theories for the unmanned aerial and ground vehicles (UAVs and UGVs). We deal with a two-dimensional nonlinear system to investigate the oscillatory behaviors of solutions. This helps us understand the limiting behavior of such solutions and contributes several theoretical results to the literature.","PeriodicalId":356825,"journal":{"name":"Oscillators - Recent Developments","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116311086","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-05-08DOI: 10.5772/INTECHOPEN.85147
Coşkun Deniz
Quantum harmonic oscillator (QHO) involves square law potential (x 2 ) in the Schrodinger equation and is a fundamental problem in quantum mechanics. It can be solved by various conventional methods such as (i) analytical methods where Hermite polynomials are involved, (ii) algebraic methods where ladder operators are involved, and (iii) approximation methods where perturbation, variational, semiclassical, etc. techniques are involved. Here we present the general outcomes of the two conventional semiclassical approximation methods: the JWKB method (named after Jeffreys, Wentzel, Kramers, and Brillouin) and the MAF method (abbreviated for “ modified Airy functions ” ) to solve the QHO in a very good precision. Although JWKB is an approximation method, it interestingly gives the exact solution for the QHO except for the classical turning points (CTPs) where it diverges as typical to the JWKB. As the MAF method, it enables very approximate wave functions to be written in terms of Airy functions without any discontinuity in the entire domain, though, it needs careful treatment since Airy functions exhibit too much oscillatory behavior. Here, we make use of the parity conditions of the QHO to find the exact JWKB and approximate MAF solutions of the QHO within the capability of these methods.
{"title":"Quantum Harmonic Oscillator","authors":"Coşkun Deniz","doi":"10.5772/INTECHOPEN.85147","DOIUrl":"https://doi.org/10.5772/INTECHOPEN.85147","url":null,"abstract":"Quantum harmonic oscillator (QHO) involves square law potential (x 2 ) in the Schrodinger equation and is a fundamental problem in quantum mechanics. It can be solved by various conventional methods such as (i) analytical methods where Hermite polynomials are involved, (ii) algebraic methods where ladder operators are involved, and (iii) approximation methods where perturbation, variational, semiclassical, etc. techniques are involved. Here we present the general outcomes of the two conventional semiclassical approximation methods: the JWKB method (named after Jeffreys, Wentzel, Kramers, and Brillouin) and the MAF method (abbreviated for “ modified Airy functions ” ) to solve the QHO in a very good precision. Although JWKB is an approximation method, it interestingly gives the exact solution for the QHO except for the classical turning points (CTPs) where it diverges as typical to the JWKB. As the MAF method, it enables very approximate wave functions to be written in terms of Airy functions without any discontinuity in the entire domain, though, it needs careful treatment since Airy functions exhibit too much oscillatory behavior. Here, we make use of the parity conditions of the QHO to find the exact JWKB and approximate MAF solutions of the QHO within the capability of these methods.","PeriodicalId":356825,"journal":{"name":"Oscillators - Recent Developments","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115615865","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-12-14DOI: 10.5772/INTECHOPEN.81865
V. Yurchenko, L. Yurchenko
We develop time-domain approach for simulation of microstrip-connected extremely-high frequency (EHF) solid-state oscillators for close-range radars, including ultrashort-pulse, ultrawide-band (UWB), and noise radars. The circuits utilize high-speed GaN-based active devices such as Gunn diodes (GD) and resonant-tunneling diodes (RTD) capable of operating with enhanced power output. Microstrip interconnects produce time-delay coupling in the system that can create a complicated nonlinear dynamics of oscillations. The circuits can generate self-emerging trains of ultra-short EHF pulses emitted into an open microstrip section for further radiation. The arrays of active devices connected in either parallel (star-case) or series (ladder-case) type of circuits were simulated. Options for generation of chaotic signals in this kind of systems have been considered. An infrared-microwave (IR-EHF) oscillator linked to the resonant antenna was simulated. The oscillator consists of an RTD-driven laser diode (LD) joint to the EHF resonant antenna with a short piece of microstrip section. The oscillator can generate both the EHF pulse radiation and the EHF modulated IR pulses. Both kinds of radiation can be emitted in the free space as the trains of correlated IR-EHF radar pulses. Arrays of oscillators can be used for enhancing the power output of the system.
{"title":"Time-Domain Simulation of Microstrip-Connected Solid-State Oscillators for Close-Range Noise Radar Applications","authors":"V. Yurchenko, L. Yurchenko","doi":"10.5772/INTECHOPEN.81865","DOIUrl":"https://doi.org/10.5772/INTECHOPEN.81865","url":null,"abstract":"We develop time-domain approach for simulation of microstrip-connected extremely-high frequency (EHF) solid-state oscillators for close-range radars, including ultrashort-pulse, ultrawide-band (UWB), and noise radars. The circuits utilize high-speed GaN-based active devices such as Gunn diodes (GD) and resonant-tunneling diodes (RTD) capable of operating with enhanced power output. Microstrip interconnects produce time-delay coupling in the system that can create a complicated nonlinear dynamics of oscillations. The circuits can generate self-emerging trains of ultra-short EHF pulses emitted into an open microstrip section for further radiation. The arrays of active devices connected in either parallel (star-case) or series (ladder-case) type of circuits were simulated. Options for generation of chaotic signals in this kind of systems have been considered. An infrared-microwave (IR-EHF) oscillator linked to the resonant antenna was simulated. The oscillator consists of an RTD-driven laser diode (LD) joint to the EHF resonant antenna with a short piece of microstrip section. The oscillator can generate both the EHF pulse radiation and the EHF modulated IR pulses. Both kinds of radiation can be emitted in the free space as the trains of correlated IR-EHF radar pulses. Arrays of oscillators can be used for enhancing the power output of the system.","PeriodicalId":356825,"journal":{"name":"Oscillators - Recent Developments","volume":"659 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116096643","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-11-12DOI: 10.5772/INTECHOPEN.81858
R. Parovik
The chapter proposes a mathematical model for a wide class of hereditary oscillators, which is a Cauchy problem in the local formulation. As an initial model equation, an integrodifferential equation of Voltaire type was introduced, which was reduced by means of a special choice of difference kernels to a differential equation with nonlocal derivatives of fractional-order variables. An explicit finite-difference scheme is proposed, and questions of its stability and convergence are investigated. A computer study of the proposed numerical algorithm on various test examples of the hereditary oscillators Airy, Duffing, and others was carried out. Oscillograms and phase trajectories are plotted and constructed.
{"title":"Mathematical Models of Oscillators with Memory","authors":"R. Parovik","doi":"10.5772/INTECHOPEN.81858","DOIUrl":"https://doi.org/10.5772/INTECHOPEN.81858","url":null,"abstract":"The chapter proposes a mathematical model for a wide class of hereditary oscillators, which is a Cauchy problem in the local formulation. As an initial model equation, an integrodifferential equation of Voltaire type was introduced, which was reduced by means of a special choice of difference kernels to a differential equation with nonlocal derivatives of fractional-order variables. An explicit finite-difference scheme is proposed, and questions of its stability and convergence are investigated. A computer study of the proposed numerical algorithm on various test examples of the hereditary oscillators Airy, Duffing, and others was carried out. Oscillograms and phase trajectories are plotted and constructed.","PeriodicalId":356825,"journal":{"name":"Oscillators - Recent Developments","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116339978","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-11-10DOI: 10.5772/INTECHOPEN.81904
Yonggang Tan
Many kinds of oscillators, springs, and damping system compose vibration reduction system in civil structures. Since the invention of the tuned mass damper (TMD) device a century ago, it has become a very important technology in structural control. TMDs can effectively suppress the response of civil structures under harmonic or wind excitations. To improve the damping capacity of TMDs in reducing the vibration of structures under seismic loads, a large mass ratio should be used, but TMDs are still ineffective in suppressing the seismic peak response of high-rise buildings. The inerter-based dynamic vibration absorbers (IDVA), including tuned inerter dampers (TID) and tuned mass-damper-inerter (TMDI), have been investigated in recent years. The advantage of using a TID and TMDI comes from the adoption of gearing in the inerter, which equivalently amplifies the mass. The mass ratio of an inerter is very high; hence, its mechanical properties and reliability are vital. A novel damper device, accelerated oscillator damper (AOD), has been proposed recently. Gear transmission systems are used to generate an amplified kinetic energy of the oscillator to reduce the oscillations of the structures. The AOD system is superior to the traditional TMD system in short time loading intervals or under the maximum seismic loads.
{"title":"Oscillator Dampers in Civil Structures","authors":"Yonggang Tan","doi":"10.5772/INTECHOPEN.81904","DOIUrl":"https://doi.org/10.5772/INTECHOPEN.81904","url":null,"abstract":"Many kinds of oscillators, springs, and damping system compose vibration reduction system in civil structures. Since the invention of the tuned mass damper (TMD) device a century ago, it has become a very important technology in structural control. TMDs can effectively suppress the response of civil structures under harmonic or wind excitations. To improve the damping capacity of TMDs in reducing the vibration of structures under seismic loads, a large mass ratio should be used, but TMDs are still ineffective in suppressing the seismic peak response of high-rise buildings. The inerter-based dynamic vibration absorbers (IDVA), including tuned inerter dampers (TID) and tuned mass-damper-inerter (TMDI), have been investigated in recent years. The advantage of using a TID and TMDI comes from the adoption of gearing in the inerter, which equivalently amplifies the mass. The mass ratio of an inerter is very high; hence, its mechanical properties and reliability are vital. A novel damper device, accelerated oscillator damper (AOD), has been proposed recently. Gear transmission systems are used to generate an amplified kinetic energy of the oscillator to reduce the oscillations of the structures. The AOD system is superior to the traditional TMD system in short time loading intervals or under the maximum seismic loads.","PeriodicalId":356825,"journal":{"name":"Oscillators - Recent Developments","volume":"159 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124455960","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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